Understanding chimney leaks
The crown of a masonry chimney is a concrete top that ideally looks something like the one shown. It has an angled top to shed water and it overhangs the brick to keep drips off the chimney sides. It surrounds the clay flues but doesn't encase them. A 1/4-in. gap allows the clay flues to expand and contract from repeated heating and cooling without cracking (or cracking the crown). (The flues “float” inside the brick chimney walls; that is, they're supported by the brick but not attached to it.) A high-quality polyurethane caulk seals the flue/crown gap and prevents water penetration.
In truth, few chimneys built before the mid-1980s have crowns built this well. Many early crowns were simply sloped washes of leftover mortar. Most have cracked and deteriorated, opening gaps around the flues. If you feel safe and confident about walking on your roof, climb up and inspect the crown. If it's sound, caulk cracks and gaps with polyurethane. Otherwise, hire a chimney builder (search online or for “Chimney Builders and Repair” in your yellow pages) or a chimney sweep (“Chimney Cleaning”) certified by the Chimney Safety Institute to evaluate the condition of your chimney and fix it. Flue caps will help reduce water coming down the flue itself, but they won't help much if you have a bad crown.